Nonlinear Plasma Dynanics in the Plasma Wakefield Accelerator

Excitation of nonlinear plasma oscillations by an ultrarelativistic electron beam is considered in this paper. It is shown, by analytical solutions of the fully relativistic nonlinear fluid equations in one dimension, that under certain conditions on the relative densities of the electron beam and the plasma, extremely large longitudinal electric fields can be generated in the wake of the beam. This scheme can be considered as a nonlinear regime of the plasma wakefield accelerator (PWFA), and is seen to have the advantage that the transformer ratio, the ratio of the maximum amplitude of the accelerating field behind the driving beam over the maximum amplitude of the decelerating field inside of the beam, can be made arbitrarily large, dependent only on the length of the driving beam. The effects of beam loading on the efficiency of this scheme are considered, and are shown to be equivalent to those predicted in the linear regime.